Consider the following two statements: (A) Linear momentum of the system remains constant. (B) Centre of mass of the system remains at rest.

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KollegeApply · Accepted Answer

B implies A but A does not imply B. The centre of mass of a system is given by, \vec{R} = 1/M \sum_{} m_i \vec{r}_i On differentiating the above equation with respect to time, we get: \frac{d \vec{R}}{dt} = 1/M \sum_{} m_i \frac{d \vec{r}_i}{d t} As the centre of mass of the system remains at rest, we have: 1/M \sum_{} m_i \frac{d \vec{r}_i}{d t} = 0 \sum_{} m_i \vec{v}_i = 0 This implies that the linear momentum of the system remains constant.

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